Interferometry makes use of superposition of electromagnetic waves with substantially the same frequency, to produce an interference pattern. Specifics of the interference pattern are due to the phase difference between the waves. Waves that are in phase undergo constructive interference while waves that are out of phase undergo destructive interference.
Typical interferometry methods, such as the well-known Michelson configuration, split a single incoming beam of coherent light into two substantially identical beams using a beam splitter such as a partially reflecting mirror. Each of the resultant beams is made to travel a different route, called a path. The two beams are then recombined at a detector. The difference in the path lengths traveled by each beam before reaching the detector creates a phase difference between beams, which can produce an interference pattern from the recombined beams. In general, any environmental condition encountered in the path of either or both beam(s) that alters the phase of the beam(s) (e.g., a change in the index of refraction of the path) prior to reaching the detector can produce an interference pattern and may impact the details thereof. Therefore, specific properties of the interference pattern can be assessed as indicators of any changes occurring along the path(s).
Very often, interference is detected using a spectrometer that separates wavelengths of light to produce a fringe pattern. Fringes are conventionally described as the light and dark bands produced by the interference of light. The regions of higher intensity (brighter bands) are generally caused by constructive superposition of the beams and the lower intensity (darker bands) regions are generally caused by destructive superposition. In the context of a graphical representation of intensity vs. wavelength (as depicted in FIG. 1A, for example) a fringe spectrum includes one or more fringe cycles. A fringe cycle can be described as a portion of the spectrum or corresponding waveform from one point of local maximum intensity e.g., the point “A” to the adjacent point of maximum intensity, e.g., point “B.” The distance between these two points represents a full period of the fringe cycle. In general, a portion of the waveform corresponding to a fringe spectrum location between any two points on the waveform that are separated by one period and the intensity measurements corresponding to that waveform represent a full fringe cycle.
Interferometers generally measure an optical path length which is the product of physical distance and refractive index. As such, interferometers can be used to sense changes in either the physical distance or the refractive index. The term optical path length typically encompasses both refractive index and distance though, typically, only one may be varied and/or measured.
As described above, an absolute difference in light paths can generate an interference pattern also called a fringe pattern. As the absolute optical path difference changes, the fringe pattern also changes. The change in the fringe pattern can be periodic, i.e., the pattern repeats when the absolute path difference changes by one wavelength (e.g., by λ0, which can be any one of the N wavelengths in the spectrum—e.g., the smallest, median, or the largest wavelength. A periodically changing fringe pattern can be called a fringe sequence.
Though the fringe pattern repeats, some associated parameter (e.g., fringe spacing) typically changes in a measurable way so that a fringe number m can be determined. The fringe spacing can be the spacing between adjacent peaks in the fringe spectrum. Techniques such as Fourier transform or linear fit can be used to compute an absolute path length difference and a corresponding fringe number and quadrant q. The absolute optical path length difference is approximately equal to (m+q)λ0, where m is an integer and q is equal to 0, ¼, ½, or ¾.
Absolute measurement (frequency domain) techniques generally uses a spectrometer as the detector, and can be used to determine m and q described above. These techniques can provide a coarse estimate of the absolute optical path length difference, but the resolution to these techniques is low—typically no better than λ0/100. Low-resolution relative phase techniques can be used as refinements to improve the resolution to as good as λo/1000. In these techniques, wavelength shifts of the spectral peaks are typically monitored and used to estimate path difference relative to a fringe. The resolution of these combined techniques, however, is still not as good as that of the highest-resolution relative phase techniques, which may have resolution as high as λo/100,000.
High-resolution relative phase techniques generally use three or more points/samples in a fringe spectrum. Traditionally in these techniques, these points/samples must be located in quadrature. Using these quadrature-spaced points, a high resolution relative measurement of the optical path difference, i.e., measurement of the optical path difference relative to a certain fringe, can be obtained. In other words, this technique can precisely determine ϕ such that the absolute optical path length difference is approximately equal to (m+q+ϕ/2π)λo. But, alone, this technique does not determine m and q and, as such, does not provide information on absolute path length difference.
The high resolution relative phase technique discussed above also cannot be combined with the absolute measurement techniques, because the high resolution relative phase technique requires approximately quadrature-spaced points from the fringe spectrum. Absolute path length measurement techniques, however, often uses a spectrometer as the detector, which does not reliably provide approximately quadrature-spaced points. Instead, a spectrometer generally provides a fringe spectrum that includes only non-quadrature-spaced samples/points. To obtain the quadrature-spaced points, high resolution relative phase techniques typically employ some device other than a spectrometer, but then, absolute path length information cannot be readily obtained. In addition, these other devices are generally expensive and complex, which can significantly increase the cost and/or complexity of obtaining absolute optical path length difference measurements. Therefore, an improved system and method is needed to facilitate accurate high resolution absolute optical path length difference measurements in an efficient manner.